Ecuaciones de segundo grado PDF

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Ecuaciones de 2 grado...

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Resolver Cuadráticas (A) Resuelva cada ecuación en función de x.

1.

2x² + 14x + 3 = -17

7.

2x² - 9x - 51 = 5

2.

2x² + 2x - 3 = 1

8.

2x² + x - 5 = 10

3.

4x² - 28x + 43 = -2

9.

x² - 7x + 4 = -6

4.

2x² - 16x + 24 = 0

10.

2x² - 17x + 15 = -15

5.

2x² - 18x + 8 = -8

11.

2x² - 9x + 3 = -6

6.

4x² - 32x + 9 = -55

12.

2x² - x - 1 = 0

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Resolver Cuadráticas (A) Respuestas Resuelva cada ecuación en función de x.

1.

2x² + 14x + 3 = -17 2x² + 14x + 20 = 0 (2x + 4) (x + 5) = 0 x = -2 , -5

7.

2x² - 9x - 51 = 5 2x² - 9x - 56 = 0 (x - 8) (2x + 7) = 0 x = 8 , -3 1/2

2.

2x² + 2x - 3 = 1 2x² + 2x - 4 = 0 (x + 2) (2x - 2) = 0 x = -2 , 1

8.

2x² + x - 5 = 10 2x² + x - 15 = 0 (x + 3) (2x - 5) = 0 x = -3 , 2 1/2

3.

4x² - 28x + 43 = -2 4x² - 28x + 45 = 0 (2x - 9) (2x - 5) = 0 x = 4 1/2, 2 1/2

9.

x² - 7x + 4 = -6 x² - 7x + 10 = 0 (x - 2) (x - 5) = 0 x=2 , 5

4.

2x² - 16x + 24 = 0 2x² - 16x + 24 = 0 (x - 6) (2x - 4) = 0 x=6 , 2

10.

2x² - 17x + 15 = -15 2x² - 17x + 30 = 0 (2x - 5) (x - 6) = 0 x = 2 1/2, 6

5.

2x² - 18x + 8 = -8 2x² - 18x + 16 = 0 (x - 8) (2x - 2) = 0 x=8 , 1

11.

2x² - 9x + 3 = -6 2x² - 9x + 9 = 0 (x - 3) (2x - 3) = 0 x = 3 , 1 1/2

6.

4x² - 32x + 9 = -55 4x² - 32x + 64 = 0 (2x - 8) (2x - 8) = 0 x=4

12.

2x² - x - 1 = 0 2x² - x - 1 = 0 (2x + 1) (x - 1) = 0 x = - 1/2, 1

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Resolver Cuadráticas (B)

Resuelva cada ecuación en función de x.

1.

4x² - 26x + 29 = -7

7.

2x² - 2x - 3 = 1

2.

2x² - 19x + 26 = -19

8.

x² + 15x + 20 = -36

3.

2x² + 2x - 3 = 9

9.

2x² - 7x - 34 = 15

4.

x² + 17x + 39 = -33

10.

2x² - 10x + 4 = -8

5.

x² + x - 27 = 29

11.

x² - 2 = 2

6.

4x² - 8x - 10 = 22

12.

4x² - 12x + 4 = -4

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Resolver Cuadráticas (B) Respuestas Resuelva cada ecuación en función de x.

1.

4x² - 26x + 29 = -7 4x² - 26x + 36 = 0 (2x - 4) (2x - 9) = 0 x = 2 , 4 1/2

7.

2x² - 2x - 3 = 1 2x² - 2x - 4 = 0 (x - 2) (2x + 2) = 0 x = 2 , -1

2.

2x² - 19x + 26 = -19 2x² - 19x + 45 = 0 (x - 5) (2x - 9) = 0 x = 5 , 4 1/2

8.

x² + 15x + 20 = -36 x² + 15x + 56 = 0 (x + 7) (x + 8) = 0 x = -7 , -8

3.

2x² + 2x - 3 = 9 2x² + 2x - 12 = 0 (x + 3) (2x - 4) = 0 x = -3 , 2

9.

2x² - 7x - 34 = 15 2x² - 7x - 49 = 0 (x - 7) (2x + 7) = 0 x = 7 , -3 1/2

4.

x² + 17x + 39 = -33 x² + 17x + 72 = 0 (x + 8) (x + 9) = 0 x = -8 , -9

10.

2x² - 10x + 4 = -8 2x² - 10x + 12 = 0 (2x - 6) (x - 2) = 0 x=3 , 2

5.

x² + x - 27 = 29 x² + x - 56 = 0 (x + 8) (x - 7) = 0 x = -8 , 7

11.

x² - 2 = 2 x² - 4 = 0 (x + 2) (x - 2) = 0 x = -2 , 2

6.

4x² - 8x - 10 = 22 4x² - 8x - 32 = 0 (2x - 8) (2x + 4) = 0 x = 4 , -2

12.

4x² - 12x + 4 = -4 4x² - 12x + 8 = 0 (2x - 4) (2x - 2) = 0 x=2 , 1

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Resolver Cuadráticas (C)

Resuelva cada ecuación en función de x.

1.

4x² - 32x + 1 = -62

7.

2x² - 3x - 1 = 1

2.

4x² + 2x - 33 = 9

8.

x² - 7x + 4 = -2

3.

x² - 5x - 2 = 34

9.

2x² + 17x + 35 = 0

4.

x² - 10x + 3 = -21

10.

2x² + 20x + 25 = -7

5.

2x² - 16x + 26 = -4

11.

2x² - 25x + 19 = -53

6.

2x² - 5 = 3

12.

2x² + 23x + 27 = -18

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Resolver Cuadráticas (C) Respuestas Resuelva cada ecuación en función de x.

1.

4x² - 32x + 1 = -62 4x² - 32x + 63 = 0 (2x - 7) (2x - 9) = 0 x = 3 1/2, 4 1/2

7.

2x² - 3x - 1 = 1 2x² - 3x - 2 = 0 (x - 2) (2x + 1) = 0 x = 2 , - 1/2

2.

4x² + 2x - 33 = 9 4x² + 2x - 42 = 0 (2x - 6) (2x + 7) = 0 x = 3 , -3 1/2

8.

x² - 7x + 4 = -2 x² - 7x + 6 = 0 (x - 6) (x - 1) = 0 x=6 , 1

3.

x² - 5x - 2 = 34 x² - 5x - 36 = 0 (x - 9) (x + 4) = 0 x = 9 , -4

9.

2x² + 17x + 35 = 0 2x² + 17x + 35 = 0 (x + 5) (2x + 7) = 0 x = -5 , -3 1/2

4.

x² - 10x + 3 = -21 x² - 10x + 24 = 0 (x - 6) (x - 4) = 0 x=6 , 4

10.

2x² + 20x + 25 = -7 2x² + 20x + 32 = 0 (x + 8) (2x + 4) = 0 x = -8 , -2

5.

2x² - 16x + 26 = -4 2x² - 16x + 30 = 0 (2x - 6) (x - 5) = 0 x=3 , 5

11.

2x² - 25x + 19 = -53 2x² - 25x + 72 = 0 (x - 8) (2x - 9) = 0 x = 8 , 4 1/2

6.

2x² - 5 = 3 2x² - 8 = 0 (2x + 4) (x - 2) = 0 x = -2 , 2

12.

2x² + 23x + 27 = -18 2x² + 23x + 45 = 0 (x + 9) (2x + 5) = 0 x = -9 , -2 1/2

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Resolver Cuadráticas (D)

Resuelva cada ecuación en función de x.

1.

4x² + 30x + 39 = -15

7.

x² + 16x + 23 = -41

2.

4x² - 18x + 1 = -7

8.

x² - 10x + 15 = -1

3.

2x² + 17x - 2 = 7

9.

x² + 9x + 8 = -6

4.

x² - 15x + 35 = -21

10.

x² - 23 = 41

5.

2x² + 15x - 1 = 7

11.

2x² - 18x + 10 = -26

6.

4x² + 4x - 42 = 6

12.

2x² - 14x + 3 = -9

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Resolver Cuadráticas (D) Respuestas Resuelva cada ecuación en función de x.

1.

4x² + 30x + 39 = -15 4x² + 30x + 54 = 0 (2x + 9) (2x + 6) = 0 x = -4 1/2, -3

7.

x² + 16x + 23 = -41 x² + 16x + 64 = 0 (x + 8) (x + 8) = 0 x = -8

2.

4x² - 18x + 1 = -7 4x² - 18x + 8 = 0 (2x - 8) (2x - 1) = 0 x = 4 , 1/2

8.

x² - 10x + 15 = -1 x² - 10x + 16 = 0 (x - 2) (x - 8) = 0 x=2 , 8

3.

2x² + 17x - 2 = 7 2x² + 17x - 9 = 0 (2x - 1) (x + 9) = 0 x = 1/2, -9

9.

x² + 9x + 8 = -6 x² + 9x + 14 = 0 (x + 2) (x + 7) = 0 x = -2 , -7

4.

x² - 15x + 35 = -21 x² - 15x + 56 = 0 (x - 7) (x - 8) = 0 x=7 , 8

10.

x² - 23 = 41 x² - 64 = 0 (x - 8) (x + 8) = 0 x = 8 , -8

5.

2x² + 15x - 1 = 7 2x² + 15x - 8 = 0 (2x - 1) (x + 8) = 0 x = 1/2, -8

11.

2x² - 18x + 10 = -26 2x² - 18x + 36 = 0 (x - 6) (2x - 6) = 0 x=6 , 3

6.

4x² + 4x - 42 = 6 4x² + 4x - 48 = 0 (2x - 6) (2x + 8) = 0 x = 3 , -4

12.

2x² - 14x + 3 = -9 2x² - 14x + 12 = 0 (x - 6) (2x - 2) = 0 x=6 , 1

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Resolver Cuadráticas (E)

Resuelva cada ecuación en función de x.

1.

2x² + 14x - 6 = 10

7.

2x² + 4x - 38 = 10

2.

x² - 5x - 6 = 8

8.

2x² + 15x - 15 = 12

3.

2x² + 15x = -7

9.

2x² + 6x - 4 = 32

4.

2x² - 22x + 15 = -21

10.

4x² - 2x - 16 = 4

5.

2x² - 12x + 8 = -10

11.

2x² + 9x - 1 = 4

6.

2x² + 16x + 26 = -4

12.

2x² - 20x + 7 = -41

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Resolver Cuadráticas (E) Respuestas Resuelva cada ecuación en función de x.

1.

2x² + 14x - 6 = 10 2x² + 14x - 16 = 0 (2x - 2) (x + 8) = 0 x = 1 , -8

7.

2x² + 4x - 38 = 10 2x² + 4x - 48 = 0 (x + 6) (2x - 8) = 0 x = -6 , 4

2.

x² - 5x - 6 = 8 x² - 5x - 14 = 0 (x + 2) (x - 7) = 0 x = -2 , 7

8.

2x² + 15x - 15 = 12 2x² + 15x - 27 = 0 (2x - 3) (x + 9) = 0 x = 1 1/2, -9

3.

2x² + 15x = -7 2x² + 15x + 7 = 0 (2x + 1) (x + 7) = 0 x = - 1/2, -7

9.

2x² + 6x - 4 = 32 2x² + 6x - 36 = 0 (x + 6) (2x - 6) = 0 x = -6 , 3

4.

2x² - 22x + 15 = -21 2x² - 22x + 36 = 0 (x - 9) (2x - 4) = 0 x=9 , 2

10.

4x² - 2x - 16 = 4 4x² - 2x - 20 = 0 (2x - 5) (2x + 4) = 0 x = 2 1/2, -2

5.

2x² - 12x + 8 = -10 2x² - 12x + 18 = 0 (2x - 6) (x - 3) = 0 x=3

11.

2x² + 9x - 1 = 4 2x² + 9x - 5 = 0 (2x - 1) (x + 5) = 0 x = 1/2, -5

6.

2x² + 16x + 26 = -4 2x² + 16x + 30 = 0 (2x + 6) (x + 5) = 0 x = -3 , -5

12.

2x² - 20x + 7 = -41 2x² - 20x + 48 = 0 (2x - 8) (x - 6) = 0 x=4 , 6

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Resolver Cuadráticas (F)

Resuelva cada ecuación en función de x.

1.

x² + 8x - 2 = 7

7.

4x² - 6x + 2 = 0

2.

2x² - 14x + 11 = -1

8.

x² - x - 21 = 9

3.

2x² + x - 1 = 2

9.

2x² - 17x + 17 = -19

4.

4x² - 14x + 2 = -4

10.

x² + x - 25 = 17

5.

2x² - 15x + 18 = -10

11.

x² - 15x + 31 = -25

6.

2x² - 10x - 42 = 6

12.

2x² + 24x + 6 = -58

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Resolver Cuadráticas (F) Respuestas Resuelva cada ecuación en función de x.

1.

x² + 8x - 2 = 7 x² + 8x - 9 = 0 (x - 1) (x + 9) = 0 x = 1 , -9

7.

4x² - 6x + 2 = 0 4x² - 6x + 2 = 0 (2x - 1) (2x - 2) = 0 x = 1/2, 1

2.

2x² - 14x + 11 = -1 2x² - 14x + 12 = 0 (x - 6) (2x - 2) = 0 x=6 , 1

8.

x² - x - 21 = 9 x² - x - 30 = 0 (x - 6) (x + 5) = 0 x = 6 , -5

3.

2x² + x - 1 = 2 2x² + x - 3 = 0 (x - 1) (2x + 3) = 0 x = 1 , -1 1/2

9.

2x² - 17x + 17 = -19 2x² - 17x + 36 = 0 (x - 4) (2x - 9) = 0 x = 4 , 4 1/2

4.

4x² - 14x + 2 = -4 4x² - 14x + 6 = 0 (2x - 1) (2x - 6) = 0 x = 1/2, 3

10.

x² + x - 25 = 17 x² + x - 42 = 0 (x + 7) (x - 6) = 0 x = -7 , 6

5.

2x² - 15x + 18 = -10 2x² - 15x + 28 = 0 (2x - 7) (x - 4) = 0 x = 3 1/2, 4

11.

x² - 15x + 31 = -25 x² - 15x + 56 = 0 (x - 8) (x - 7) = 0 x=8 , 7

6.

2x² - 10x - 42 = 6 2x² - 10x - 48 = 0 (2x + 6) (x - 8) = 0 x = -3 , 8

12.

2x² + 24x + 6 = -58 2x² + 24x + 64 = 0 (x + 8) (2x + 8) = 0 x = -8 , -4

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Resolver Cuadráticas (G)

Resuelva cada ecuación en función de x.

1.

x² + 11x + 14 = -4

7.

2x² - 27x + 8 = -73

2.

4x² + 18x + 14 = -6

8.

2x² + x - 22 = 6

3.

2x² + x - 2 = 26

9.

x² - 13x + 36 = 0

4.

2x² - 27 = 5

10.

2x² + 10x - 10 = 38

5.

2x² + 3x - 30 = 5

11.

2x² + 3x - 41 = 13

6.

x² + 10x + 21 = 0

12.

2x² - 13x - 17 = 7

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Resolver Cuadráticas (G) Respuestas Resuelva cada ecuación en función de x.

1.

x² + 11x + 14 = -4 x² + 11x + 18 = 0 (x + 9) (x + 2) = 0 x = -9 , -2

7.

2x² - 27x + 8 = -73 2x² - 27x + 81 = 0 (2x - 9) (x - 9) = 0 x = 4 1/2, 9

2.

4x² + 18x + 14 = -6 4x² + 18x + 20 = 0 (2x + 4) (2x + 5) = 0 x = -2 , -2 1/2

8.

2x² + x - 22 = 6 2x² + x - 28 = 0 (2x - 7) (x + 4) = 0 x = 3 1/2, -4

3.

2x² + x - 2 = 26 2x² + x - 28 = 0 (x + 4) (2x - 7) = 0 x = -4 , 3 1/2

9.

x² - 13x + 36 = 0 x² - 13x + 36 = 0 (x - 4) (x - 9) = 0 x=4 , 9

4.

2x² - 27 = 5 2x² - 32 = 0 (2x - 8) (x + 4) = 0 x = 4 , -4

10.

2x² + 10x - 10 = 38 2x² + 10x - 48 = 0 (x + 8) (2x - 6) = 0 x = -8 , 3

5.

2x² + 3x - 30 = 5 2x² + 3x - 35 = 0 (2x - 7) (x + 5) = 0 x = 3 1/2, -5

11.

2x² + 3x - 41 = 13 2x² + 3x - 54 = 0 (x + 6) (2x - 9) = 0 x = -6 , 4 1/2

6.

x² + 10x + 21 = 0 x² + 10x + 21 = 0 (x + 7) (x + 3) = 0 x = -7 , -3

12.

2x² - 13x - 17 = 7 2x² - 13x - 24 = 0 (x - 8) (2x + 3) = 0 x = 8 , -1 1/2

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Resolver Cuadráticas (H)

Resuelva cada ecuación en función de x.

1.

2x² + 8x = -6

7.

2x² - 8x + 6 = 0

2.

4x² + 20x = -9

8.

4x² - 16x = -7

3.

2x² + 2x - 7 = 17

9.

2x² - 11x + 1 = -4

4.

2x² - x - 3 = 12

10.

4x² - 16x + 5 = -7

5.

x² + 7x - 5 = 13

11.

2x² + 4x - 11 = 5

6.

4x² - 22x + 5 = -23

12.

4x² - 14x - 5 = 13

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Resolver Cuadráticas (H) Respuestas Resuelva cada ecuación en función de x.

1.

2x² + 8x = -6 2x² + 8x + 6 = 0 (x + 3) (2x + 2) = 0 x = -3 , -1

7.

2x² - 8x + 6 = 0 2x² - 8x + 6 = 0 (x - 3) (2x - 2) = 0 x=3 , 1

2.

4x² + 20x = -9 4x² + 20x + 9 = 0 (2x + 9) (2x + 1) = 0 x = -4 1/2, - 1/2

8.

4x² - 16x = -7 4x² - 16x + 7 = 0 (2x - 1) (2x - 7) = 0 x = 1/2, 3 1/2

3.

2x² + 2x - 7 = 17 2x² + 2x - 24 = 0 (x - 3) (2x + 8) = 0 x = 3 , -4

9.

2x² - 11x + 1 = -4 2x² - 11x + 5 = 0 (2x - 1) (x - 5) = 0 x = 1/2, 5

4.

2x² - x - 3 = 12 2x² - x - 15 = 0 (x - 3) (2x + 5) = 0 x = 3 , -2 1/2

10.

4x² - 16x + 5 = -7 4x² - 16x + 12 = 0 (2x - 2) (2x - 6) = 0 x=1 , 3

5.

x² + 7x - 5 = 13 x² + 7x - 18 = 0 (x + 9) (x - 2) = 0 x = -9 , 2

11.

2x² + 4x - 11 = 5 2x² + 4x - 16 = 0 (2x + 8) (x - 2) = 0 x = -4 , 2

6.

4x² - 22x + 5 = -23 4x² - 22x + 28 = 0 (2x - 7) (2x - 4) = 0 x = 3 1/2, 2

12.

4x² - 14x - 5 = 13 4x² - 14x - 18 = 0 (2x - 9) (2x + 2) = 0 x = 4 1/2, -1

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Resolver Cuadráticas (I)

Resuelva cada ecuación en función de x.

1.

2x² - 11x + 8 = -1

7.

2x² - 19x + 23 = -12

2.

2x² + 11x + 5 = -7

8.

2x² + 3x - 16 = 19

3.

x² + 9x + 4 = -14

9.

2x² + 17x + 30 = -5

4.

x² + 3x - 12 = 16

10.

2x² + 4x - 10 = 6

5.

2x² + 20x + 13 = -5

11.

2x² + 16x + 28 = -2

6.

x² - 13x + 15 = -21

12.

2x² - 13x + 10 = -8

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Resolver Cuadráticas (I) Respuestas Resuelva cada ecuación en función de x.

1.

2x² - 11x + 8 = -1 2x² - 11x + 9 = 0 (x - 1) (2x - 9) = 0 x = 1 , 4 1/2

7.

2x² - 19x + 23 = -12 2x² - 19x + 35 = 0 (x - 7) (2x - 5) = 0 x = 7 , 2 1/2

2.

2x² + 11x + 5 = -7 2x² + 11x + 12 = 0 (2x + 3) (x + 4) = 0 x = -1 1/2, -4

8.

2x² + 3x - 16 = 19 2x² + 3x - 35 = 0 (x + 5) (2x - 7) = 0 x = -5 , 3 1/2

3.

x² + 9x + 4 = -14 x² + 9x + 18 = 0 (x + 6) (x + 3) = 0 x = -6 , -3

9.

2x² + 17x + 30 = -5 2x² + 17x + 35 = 0 (2x + 7) (x + 5) = 0 x = -3 1/2, -5

4.

x² + 3x - 12 = 16 x² + 3x - 28 = 0 (x + 7) (x - 4) = 0 x = -7 , 4

10.

2x² + 4x - 10 = 6 2x² + 4x - 16 = 0 (2x + 8) (x - 2) = 0 x = -4 , 2

5.

2x² + 20x + 13 = -5 2x² + 20x + 18 = 0 (2x + 2) (x + 9) = 0 x = -1 , -9

11.

2x² + 16x + 28 = -2 2x² + 16x + 30 = 0 (x + 5) (2x + 6) = 0 x = -5 , -3

6.

x² - 13x + 15 = -21 x² - 13x + 36 = 0 (x - 4) (x - 9) = 0 x=4 , 9

12.

2x² - 13x + 10 = -8 2x² - 13x + 18 = 0 (2x - 9) (x - 2) = 0 x = 4 1/2, 2

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Resolver Cuadráticas (J)

Resuelva cada ecuación en función de x.

1.

2x² + 9x + 1 = -3

7.

2x² - 21x + 18 = -36

2.

2x² - 15x + 2 = -23

8.

2x² + 23x + 27 = -29

3.

2x² - 6x - 5 = 15

9.

2x² - 13x + 4 = -2

4.

4x² - 14x + 9 = -3

10.

4x² - 30x + 6 = -50

5.

x² - 2x - 1 = 14

11.

4x² - 20x = -9

6.

2x² - 22x + 4 = -32

12.

4x² + 6x - 2 = 8

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Resolver Cuadráticas (J) Respuestas Resuelva cada ecuación en función de x.

1.

2x² + 9x + 1 = -3 2x² + 9x + 4 = 0 (2x + 1) (x + 4) = 0 x = - 1/2, -4

7.

2x² - 21x + 18 = -36 2x² - 21x + 54 = 0 (x - 6) (2x - 9) = 0 x = 6 , 4 1/2

2.

2x² - 15x + 2 = -23 2x² - 15x + 25 = 0 (x - 5) (2x - 5) = 0 x = 5 , 2 1/2

8.

2x² + 23x + 27 = -29 2x² + 23x + 56 = 0 (2x + 7) (x + 8) = 0 x = -3 1/2, -8

3.

2x² - 6x - 5 = 15 2x² - 6x - 20 = 0 (2x + 4) (x - 5) = 0 x = -2 , 5

9.

2x² - 13x + 4 = -2 2x² - 13x + 6 = 0 (2x - 1) (x - 6) = 0 x = 1/2, 6

4.

4x² - 14x + 9 = -3 4x² - 14x + 12 = 0 (2x - 3) (2x - 4) = 0 x = 1 1/2, 2

10.

4x² - 30x + 6 = -50 4x² - 30x + 56 = 0 (2x - 7) (2x - 8) = 0 x = 3 1/2, 4

5.

x² - 2x - 1 = 14 x² - 2x - 15 = 0 (x + 3) (x - 5) = 0 x = -3 , 5

11.

4x² - 20x = -9 4x² - 20x + 9 = 0 (2x - 1) (2x - 9) = 0 x = 1/2, 4 1/2

6.

2x² - 22x + 4 = -32 2x² - 22x + 36 = 0 (x - 9) (2x - 4) = 0 x=9 , 2

12.

4x² + 6x - 2 = 8 4x² + 6x - 10 = 0 (2x + 5) (2x - 2) = 0 x = -2 1/2, 1

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